Non-Locality$\neq$Quantum Entanglement

TL;DR

This paper challenges the assumption that quantum entanglement directly correlates with non-locality, showing through extended analysis that they are not equivalent, and proposes a new method for diagnosing entanglement.

Contribution

The paper introduces a generalized R-matrix for diagnosing quantum entanglement and demonstrates that entanglement and non-locality are not inherently equivalent.

Findings

Numerical results contradict the expectation that entanglement correlates with non-locality.

The generalized R-matrix restores the monotonic relationship between entanglement and non-locality.

Entanglement and non-locality are shown to be distinct phenomena.

Abstract

The unique entanglement measure is concurrence in a 2-qubit pure state. The maximum violation of Bell's inequality is monotonically increasing for this quantity. Therefore, people expect that pure state entanglement is relevant to the non-locality. For justification, we extend the study to three qubits. We consider all possible 3-qubit operators with a symmetric permutation. When only considering one entanglement measure, the numerical result contradicts expectation. Therefore, we conclude ``Non-Locality$\neq$Quantum Entanglement''. We propose the generalized $R$-matrix or correlation matrix for the new diagnosis of Quantum Entanglement. We then demonstrate the evidence by restoring the monotonically increasing result.